The Incumbency Advantage in Judicial Elections

Transcription

1 The Incumbency Advantage in Judicial Elections Michael Olson and Andrew R. Stone September 10, 2018 This is an early draft. Please do not cite without permission. Abstract Political scientists and legal scholars debate the value of judicial elections. Proponents of electing judges highlight the value of elections as an accountability mechanism for judicial policymakers, but descriptive evidence including low levels of electoral competition and voter participation suggests limits to this electoral connection. In this paper, we explore whether holding judicial office provides partisan judges with a built-in incumbency advantage. We assemble data on partisan, single-member district judicial elections from the U.S. states. In addition to providing new descriptive data on competitiveness in these elections, we use a regression discontinuity design to causally identify the electoral benefits of incumbency. We demonstrate that incumbents enjoy electoral advantages of more than twenty percentage points, dwarfing even the most impressive estimates of the incumbency advantage in legislative elections. These advantages are due largely to a scare-off effect, where even a narrow victory dramatically decreases the probability that a party will be challenged in the next election. Our findings highlight the sizable returns to holding judicial office and provide compelling evidence that electoral pressures are minimal for judges. Paper prepared for presentation at the 2018 Toronto Political Behaviour Workshop. Michael Olson (michaelolson@g.harvard.edu) and Andrew R. Stone (arstone@g.harvard.edu) are Ph.D. Candidates, Harvard University Department of Government.

2 One of the most unique features of American democracy is the procedure of popularly electing judges. Forty-three American states use some sort of popular elections to choose at least some of their judges, providing the American electorate with a distinctive opportunity to transmit their preferences over how judges behave directly onto the bench. Considerable debate has been devoted to whether judicial elections are beneficial or detrimental for judicial outcomes and democratic government as a whole. On the one hand, an electoral connection offers an opportunity for the public to hold their judicial public servants directly accountable for their behavior and to hand-select the judges that they wish to serve on the bench. On the other, concerns regarding the erosion of judicial independence and the inability of elected judiciaries to insulate themselves from political pressures suggests negative consequences for the outputs of the judiciary, especially when combined with descriptive evidence suggesting that voters have little interest in and knowledge of judicial elections. In this paper, we provide novel, causally-identified empirical evidence of the efficacy of judicial elections in achieving their goal of electoral accountability. To do so, we collect and analyze data from partisan judicial elections in six politically diverse U.S. states. Our focus on elections where incumbent judges that run for re-election face partisan contested elections (as opposed to retention elections) provides a strong test of the ability of judicial elections to serve as a mechanism of accountability. Our analysis reveals that even in these most accountability-oriented of electoral settings, competition is strikingly low. We show descriptively that the vast majority of these elections are not contested, that margins of victory are large, and that individuals and parties routinely hold seats for long periods of time. We also demonstrate that this is not merely a function of one-sided partisan electorates: using a regression discontinuity design, we demonstrate that even narrow victories in an initial election result in subsequent partisan incumbency advantages of more than twenty percentage points. Further analysis reveals that this built-in advantage for incumbents is driven primarily by a dramatic drop-off in the probability that an incumbent faces a contested election in the future: a scare-off" effect. 1

3 Our study makes a series of important contributions to the study of electoral politics and the judiciary. First, our data add depth to existing descriptive analyses of competition and voting behavior in judicial elections. Complementing a host of existing studies that explore patterns of competition in judicial elections in state supreme courts (e.g., Bonneau and Hall 2009), we collect data on elections for over 1,300 unique lower state court judicial seats in fifty-three state-election years. These data provide for a more comprehensive understanding of judicial competition at all levels of the judicial hierarchy and allow for novel examination of longitudinal variation in competition in partisan judicial elections. Second, our research design allows us to uncover a causal estimate of the built-in electoral advantage incumbent judges accrue via holding office. The substantively large incumbency effect we identify is devoid of potential confounding variables including candidate quality, resources and valance considerations and thus provides compelling evidence of the lack of competition in state judicial elections. Third, our findings reveal new information about the function and structure of elections more generally. The magnitude of the incumbency advantage in state judicial elections is considerably higher than in legislative contexts, both state (Fowler and Hall 2015) and federal (Lee 2008), as well as in mayoral races (de Benedictis-Kessner 2017, Appendix C). This provides evidence that the salience of an election is associated with the incumbency advantage afforded to officeholders and adds further credence to arguments that courts are unique in their lack of competition. That much of the incumbency effect for judges is a result of a scare-off effect places judicial elections in contrast to legislative offices at both the federal and state level (Hall and Snyder 2015) and reveals important heterogeneity in the nature of the incumbency advantage across electoral settings. Electoral Competition and the Incumbency Advantage Electoral competition lies at the heart of the democratic process. The ability of the electorate to hold elected officials accountable for their behavior is limited without a choice between al- 2

4 ternatives and the possibility of voting an incumbent out of office. Although scholars debate the degree to which competitiveness leads to a Downsian convergence of candidate positions to the median voter, contested elections appear to be associated with greater responsiveness to constituent preferences across a series of electoral contexts (Ansolabehere, Snyder, and Stewart 2001; Powell 2000). These normative implications have led to the development of a literature that examines competition across electoral contexts. One key concept in this literature is that of the incumbency advantage. The presence of a built-in electoral advantage endowed to officeholders has clear implications for democratic accountability and representation. Befitting its importance, a multitude of studies have turned their attention to the incumbency advantage. Focusing primarily on legislative contexts, most prominently the U.S. House, scholars have sought to measure and quantify the incumbency advantage (Ansolabehere, Snyder, and Stewart 2000; Gelman and King 1990), track its size across time (Abramowitz 1991) and explain its sources (Levitt and Wolfram 1997) and consequences (King and Gelman 1991). A relatively recent innovation to the study of the incumbency advantage is the regression discontinuity design, in which winning candidates who fall just above the 50% vote threshold are considered, on average, equal to losing candidates who fall just below the vote threshold (Lee 2008). This research design allows the researcher to avoid explicit attempts to control for factors such as candidate quality, fundraising ability and partisan strength in the electorate and uncover a valid causal estimate of the incumbency advantage. 1 Applications of this method have added important insight into the source and nature of the incumbency advantage (e.g., Butler 2009; Fouirnaies and Hall 2014; Hall and Snyder 2015). Despite these recent innovations, scholarship on the incumbency advantage remains focused predominantly on legislative contexts (cf. de Benedictis-Kessner 2017). 1 The validity of the estimate requires, among other assumptions, that the just-winners and just-losers do not have control over whether they end up below or above the vote threshold (Caughey and Sekhon 2011; Fowler et al. 2015). 3

5 Competition and Incumbency in Judicial Elections Empirical political science has done much to establish the role of judges as political actors who seek to manifest their preferred policy outcomes through the rulings they make, subject to the constraints placed upon them by the institutions they operate within and the other political actors they interact with (e.g., Epstein and Knight 1998; Maltzman, Spriggs, and Wahlbeck 2000). Given the role of judges as policymakers, proponents of judicial elections view them as a way to allow voters a voice in selecting the judges that determine the policy they are subject to while also subjecting judges to an electoral process that renders them accountable for their behavior. But given the unique nature of judicial elections and the distinctive role (when compared with legislatures and executives) that judges play in policymaking, it is perhaps unsurprising that commentators and academics have highlighted a series of problems with these selection mechanisms. Studies that isolate problems with judicial elections fall into two general camps: problems these elections present for voters ability to effectively exercise their democratic voice and problems these elections create by shaping the incentives for judicial behavior. Empirical data suggests challenges for voters in gaining information about judicial elections (Geyh 2003; Griffin and Horan 1983), although these limitations may be mitigated by campaign spending and advertisements (Bonneau and Hall 2009; Hall 2014b). On the other side of the coin, evidence suggests that subjecting judges to electoral pressures can lead judges to act in ways that deviate from idealized versions of judicial behavior, especially with respect to the equal application of the rule of law. Huber and Gordon (2004) and Brace and Boyea (2008) find that the presence of judicial elections leads judges to become more punitive in their sentencing of criminals, although the latter shows that judges are responsive to public opinion when doing so. Students of judicial elections, much like in the case of legislative elections, bemoan the lack of competition in these contests. Competition appears to be particularly valuable in low-salience judicial elections, in which contested and close races that stimulate campaign spending and advertising have been shown to markedly increase voters knowledge and attentiveness to judicial 4

6 campaigns (Hall 2014b). Yet given the theoretical importance of competition in judicial elections, scholarship lacks a comprehensive understanding of the degree to which judges in state elections face competition. Perhaps most notably given the attention to incumbency by scholars of legislative politics, the judicial literature lacks an estimate of the incumbency advantage afforded to judges. Uncovering an estimate of this quantity would help provide important depth to accounts of these elections and help evaluate the normative claims often raised about judicial elections. Additionally, the majority of studies of judicial competition focus on state high courts (e.g., Hall 2001, 2007a), which leaves unanswered questions about the degree to which competition in lower courts parallels these findings. Data and Methods The American judiciary and judicial elections come in a wide variety of forms. The structure and jurisdiction of state high courts typically resembles that of the U.S. Supreme Court, although important variation across states exists. At the lower court level, however, the institutional structure across states is diverse and multifaceted. Courts may be organized by districts, counties, substantive jurisdictions, or some combination of the three, typically with a general primary jurisdiction trial court and appellate level hierarchical structure. The judges that fill these various courts are selected through a variety of means. Only seven states do not elect judges at all, eighteen use partisan elections for at least some offices, twenty-one use non-partisan elections, and twenty-one use retention elections, six exclusively. This variation offers students of electoral politics a unique opportunity to examine the prospects of alternative judicial selection procedures in generating accountability and normatively desirable outcomes; it also reflects the broad lack of consensus on the best means to achieve these. In this paper, we focus on single-member seat partisan elections. This is for three reasons. First, these are the elections that, theoretically, ought to offer the greatest prospects for account- 5

7 ability and competition. While most or all state-level judicial elections are low-information environments, party labels carry a huge quantity of information for voters to use in making a decision (Anthony 1957; Lau and Redlawsk 2001), thus dramatically increasing information available for voters to use over non-partisan or retention elections. Unlike the latter category, partisan elections also (potentially) pit candidates against each other; previous scholarship has demonstrated that this has a discernible effect on the behavior of judges (Gordon and Huber 2007) and voters (Hall 2014a). A second reason is because this sample of elections allows us to use existing methods for recovering causal estimates of the (partisan) incumbency advantage. In querying the capacity of elections to hold representatives accountable, a consistent measure in the literature has been the benefit that accrues to incumbents simply by holding office. The incumbency advantage is normatively troubling insofar as it reduces the need for incumbents to be accountable to constituents (King and Gelman 1991) and can lead to pathological behavior by those holding elected office (Fiorina 1989). A final motivation to use this sample of data is that little is known about the nature of sub-state-level partisan judicial elections. Despite being used in more than 20% of states, little is known about the partisan breakdown and competitiveness of these races. We offer new descriptive statistics to fill this informational gap. Our data come from six states Alabama, Indiana, Kansas, Missouri, Texas, and West Virginia that hold partisan elections and contested partisan elections for incumbents (rather than retention elections) to fill single court seats that have only one seat up for election at a time. 2 Our sample includes district courts, circuit courts, magistrate courts, and county courts, with electorates ranging from less than 10,000 to well over 100,000. While our earliest results come from 1952, the bulk of the data is from 1992 onward. The specific sample of data, including court-specific years and observation counts, can be found in Table A.1 in the Supplementary Materials. We structure our data in a court-by-election panel dataset, which allows us to make inferences based 2 For many courts, especially Supreme Courts, multiple seats are elected at one time, complicating a direct analysis of the effect of incumbency. 6

8 Count Democratic Vote Share Figure 1: Democratic Vote Share, Partisan Judicial Elections on temporally adjacent elections in the same state and court district. 3 Descriptive Evidence We begin our exploration of the data by offering novel descriptive information about these elections. We first note that the vast majority of the partisan judicial elections that we consider are uncontested. Figure 1 plots the Democratic candidate s share of the vote for each of the 5161 races in our data. As this figure makes clear, the vast majority of these races are wholly uncompetitive. More than 2,500 races are uncontested Republican victories and more than 1,500 are uncontested Democratic victories. This leaves only 1114 races, or 22 % of our sample, as contested. These findings reinforce and extend existing evidence from state high courts about the lack of competition in judicial elections (Hall 2007a), suggesting even greater challenges to judicial competition at the lower levels of the judicial hierarchy. 3 To allow us to focus on partisan competition, we focus throughout the paper on the two-party vote share. To avoid issues with use of the two-party vote share, we omit any race in which third-party, independent, or write-in candidates received more than 15% of the vote. 7

9 We next present an analogous figure for the incumbent party s vote share. This is presented in its entirety in Figure 2a. This figure provides evidence along two dimensions. The first is that incumbent parties generally fair quite well in these partisan judicial elections; indeed, in nearly 3,000 races in our sample the incumbent wins in uncontested fashion; even when contested, the incumbent does notably better than a coin-flip. The second motivation for presenting this figure, and in particular the version of the histogram focused on contested elections presented in Figure 2b, is to demonstrate that incumbents do not seem to be uniquely able to win close elections that is, to manipulate the running variable. Were this the case, the assumptions regarding a regressiondiscontinuity design, which we discuss and use below, would be invalid. Caughey and Sekhon (2011) demonstrate that this is an issue with certain samples of U.S. House races; fortunately, the smooth transition across the electoral cutpoint demonstrated in Figure 2b suggest that this is not a problem in our sample Count Count Incumbent Party Vote Share (a) Full Histogram Incumbent Party Vote Share (b) Cutpoint Detail Figure 2: Incumbent Party Vote Share In the Supplementary Materials, we provide additional descriptive data that is somewhat orthogonal to our purpose in the paper, but which interested readers may wish to see. In Figure A.1, we show over-time patterns of Democratic vote share in each of the states that comprise our sample, and in Figure A.2 we show an analogous plot for the average incumbent vote share in each state. Finally, Figure A.3 presents histograms of the Democratic vote share for each state. 8

10 Empirical Strategy One of the most-studied phenomena in American politics is the electoral advantage that accrues to incumbents solely by dint of their office-holding status. Long-studied solely in the context of the U.S. House of Representatives (Erikson 1971), subsequent scholarship has identified the existence of an incumbency advantage across elected offices in the United States (Ansolabehere and Snyder Jr 2002). While recent work has highlighted the possibility that the existence of an incumbency advantage merely reflects an election process that accurately selects higher-quality candidates (Ashworth and Bueno de Mesquita 2008; Eggers 2017), most work assumes that voter use of incumbency as a cue is undesirable and potentially contributing to the weakening of the candidate pool, the exertion of non-programmatic effort by elected officials, and the insulation of candidates from constituent pressures and concerns. In this section, we describe our implementation of a regression discontinuity design, following Lee (2008) and others, to evaluate the causal effect of incumbent status on subsequent vote shares. In short, we evaluate whether victory in one period by the narrowest of margins is associated with a larger margin of victory for that party in subsequent elections. This design has both advantages and limitations. Unlike alternative methods of measuring the incumbency advantage, we do not require a benchmark" party vote total: other studies have used measures of the normal vote" based on presidential vote shares (King and Gelman 1991), lagged candidate vote shares or fixed-effects approaches (Ansolabehere and Snyder Jr 2002). The former two measures are likely to be biased; the latter requires long panels, a particular difficulty given the long terms common in judicial elections. Our design also provides an estimate of the quantity we are most interested in: a local effect at narrow electoral victories. Our descriptive analysis above clearly demonstrates that most elections are lopsided; the impact of judicial elections in jurisdictions where party competition is most likely to be successful is what we learn from the regression discontinuity design. Aside from these advantages, the design has one significant limitation: while the incumbency advantage is generally thought to be the advantage a candidate accrues from running as an incumbent rather than a non-incumbent, this design 9

11 can capture only the partisan incumbency advantage, the benefit a party receives from having won the previous election. 4 Though this design misses this nuance, it comes at a great benefit: possible bias from candidates selecting in and out of running is eschewed through the use of this design. Estimation of regression-discontinuity designs is an ongoing area of methodological study. While many studies have relied on the use of OLS regression possibly with either or both a limited selection of data from around the cutpoint or a flexible polynomial fit of the running variable recent methodological studies have pointed to the superiority of semi- or non-parametric methods such as local linear regression (Gelman and Imbens 2018; Calonico, Cattaneo, and Titiunik 2014). In these estimation procedures, a smoothing parameter ( bandwidth") for the local linear regression is selected through cross-validation, and estimation is undertaken with this parameter. While we present more-traditional OLS results in the Supplementary Materials, our primary specification is based upon using local linear regression. We are also faced with the difficulty of pooling data across states, courts, and years. While in a regression-discontinuity design confounders including unobservable unit- or time-specific confounders are balanced across the cutpoint in expectation, this may not be true in a finite sample. While we follow the literature s advice regarding including covariates in this case, fixed effects in the design, and present results based on the untransformed data in the text, we also follow previous studies (e.g. Sances 2017) and present results in the Supplementary Materials based on outcomes de-meaned by court and year. Results In this section we present our empirical evidence for our main result: that the incumbency advantage in sub-state-level partisan judicial elections is extremely large. We begin by estab- 4 Erikson, Titiunik et al. (2015) outline the assumptions required to recover personal incumbency advantage estimates from regression-discontinuity designs. 10

12 lishing the validity of the regression discontinuity design in this context. We then present our baseline results, and discuss a number of robustness checks, results for which are presented in the Appendix. Validity of the Regression Discontinuity Design We take three main approaches to demonstrate the validity of the regression design in our sample. The first evidence is presented above, in Figure 2b. As is noted there, this histogram suggests that incumbents were not able to manipulate vote totals in their favor. This therefore functions as a version of a McCrary Density Test (McCrary 2008). As a second check, we use a placebo outcome that cannot possibly be affected by the treatment lagged Democratic vote share and demonstrate that no causal effect" is apparent when this outcome is used. Were an effect to be identified in this setting, it would suggest that balance on possible confounders is not achieved through use of the design. Fortunately, we do find no effect. These results are presented visually in Figure 3. While we also formally evaluate this placebo test in the Supplementary Materials (Figure B.1), the visual result is clear: there seems to be little to no difference in lagged Democratic vote share on the two sides of the electoral cutpoint. This suggests that, while the next election s vote share may matter a great deal on that cutpoint, the sample is balanced on lagged Democratic-voting. Finally, we evaluate another placebo test, on a different dimension: we demonstrate that a treatment effect is visible only at the true electoral cutpoint, rather than at different possible cutpoints. Intuitively, this demonstrates that we do not simply have a jumpy" sample, but rather than we identify a true treatment effect at the point of treatment assignment. We present the results which preview and spoil the main results, presented below of this placebo test in Figure 4. As the figure demonstrates, a positive outcome is visible only at the true cutpoint, 0.5; at alternatives on either side, no treatment effect is found. 11

13 1.00 Democratic Vote Share, Time = T Democratic Vote Share, Time = T Figure 3: Regression Discontinuity Placebo Check: Lagged Democratic Vote Share 12

14 0.2 Estimate Cutpoint Figure 4: Alternative Cutpoint Placebo Test Estimates are based on local linear regression RD estimation procedure with bandwidth fixed at Estimation undertaken using RDEstimate function from rd package in R. Estimate is calculated at cutpoints ranging from 0.4 to 0.6 at intervals of

15 Main Results As above, we present our results first visually. Figure 5 is analogous to the validity-check plot above, but presents the main analysis: the x-axis is the Democratic vote share in election t, the y-axis plots the Democratic vote share in election t + 1. The figure makes a number of things clear. The first is that there is a sizable partisan incumbency advantage in our sample of sub-state-level judicial elections. The second is that this appears to be driven primarily by noncompetitive elections. In competitive elections in the second period, there doesn t appear to be much of a gap across the discontinuity; looking at the extreme ranges of the y-axis, however, and the dramatic transition in uncontested election at the cutpoint becomes clear. We explore this explicitly below Democratic Vote Share, Time = T Democratic Vote Share, Time = T Figure 5: Regression Discontinuity Plot: Judicial Partisan Incumbency Advantage Formal presentation of our main results are presented in Figure 6. In this analysis, we estimate the causal effect of partisan incumbency across a variety of local linear regression bandwidths. As this figure demonstrates, across bandwidths ranging from only half a percentage point to twenty 14

16 percentage points, this estimation procedure consistently estimates a partisan incumbency advantage of greater than twenty percentage points, and perhaps as high as thirty percentage points. We also present these results in table format in the Supplementary Materials (Table B.1), to provide interested readers with more detailed information about sample sizes, point estimates, and statistical inference in the analyses Estimate Bandwidth Figure 6: Incumbency Advantage Results Estimation undertaken using RDEstimate function in R, at bandwidths ranging from to 0.2 at intervals of % confidence intervals are calculated based on state-clustered standard errors. Cognizant of the fact that our sample of states are politically and electorally distinct, we now strive to demonstrate that the relationship we document above is not a function of any particular state or court, but is rather a general feature of partisan judicial elections. To do so, we simply re-plot our main result, as in Figure 5, separately by state. 5 These results are presented 5 We do not formally evaluate the RD specification as above due to concerns about data sparsity around the cutpoint. 15

17 in Figure 7. As this makes clear, despite different amounts of data and small differences in the basic pattern we present, across all of these states a substantively large incumbency advantage is apparent. Furthermore, all of these states seem to follow the basic pattern outlined above, with the incumbency advantage being driven by uncontested elections in period t + 1. Finally, as noted above, we consider the degree to which our estimates can be explained through scare-off. The most salient prior work on this topic is the study by Hall and Snyder (2015). In that paper, they use a regression-discontinuity approach and three samples of legislative races, finding evidence of a large incumbency advantage but little evidence that partisan incumbency affects subsequent challenger quality. While we lack data on challenger quality and it is not entirely clear what this would look like in the present context the above visualizations suggest that an important feature of scare-off in our sample is not (necessarily) challenger quality, but challenger existence. To this end, we adapt Hall and Snyder s (2015) net quality" measure to our application, and take as an outcome variable DemocratRunning RepublicanRunning. Using this outcome, we re-estimate our local linear RD specification. The results are presented visually in Figure 8a, and formally in Figure 8b. As these figures make clear, even the narrowest of victories is associated with a massive swing in the likelihood of an uncontested race. In the Supplementary Materials, we present these results with outcome variables broken out by party. These results, in Figure B.2a and B.2b, show that the effect shown in Figure 8 is quite symmetric: a narrow Democratic victory is associated with an approximately 20-30% increase in the likelihood that a Democrat runs in the next election, and a 20-30% decrease in the likelihood that a Republican runs. Our results present a striking story: not only are sub-state-level judicial elections largely uncompetitive, but they are so systematically. As we demonstrate here, a party s victory in one election has important consequences for subsequent election outcomes: not only does that party have an incumbency advantage of more than twenty percentage points in subsequent elections, but they are dramatically less likely to face a challenger at all. This basic result, with only variation 16

18 Alabama Indiana Kansas Missouri 1.00 Democratic Vote Share, Time = T Texas Democratic Vote Share, Time = T Figure 7: Incumbency Advantage Results, by State 17

19 Democratic Vote Share, Time = T Estimate Democratic Vote Share, Time = T (a) RD Results: Contested Elections Bandwidth (b) Formal RD Results: Contested Elections Figure 8: Contested Elections RD Estimates in degree, appears in each state that comprises our sample. We now discuss the robustness of this result to alternative specifications. Robustness In this section, we seek to assuage any concerns that the results that we report above are a function of our specific choice of empirical specification. To this end, we present three alternative specifications. First, we present local linear regression with a two-way de-meaned outcome, to control for possible imbalance on court- and election-specific unobservable characteristics. Second, we re-estimate our quantities of interest using OLS regression, with a variety of bandwidths and polynomial fits of the data. Finally, we present results based on randomization inference, a method that, while identified under a stronger assumption than the results presented above, may be more suitable for relatively small datasets such as ours. De-Meaned Outcome Variable To approximate the use of court and year fixed effects while retaining the local linear regression estimation strategy, we two-way de-mean our outcome variable, the lead of Democratic vote share. We calculate the mean of this variable within year and court, and then subtract from each observation the relevant court and year means. On this transformed outcome variable, we re-estimate the specifications from above. Because this is akin to 18

20 including covariates (court and year indicator variables) in the specification, this choice strictly speaking goes against best practices in RD estimation (Calonico et al. 2016). However, it may capture any subtle imbalances in our relatively small dataset that could produce spurious results. The results are presented in the Supplementary Materials in Figure C.1, which is akin to Figure 5 above, and Figure C.2, which is akin to Figure 6 above. In both cases, the estimates are somewhat less impressive than those above, but retain the direction and substantive importance. Across most bandwidths of reasonable size, an incumbency advantage of about twenty percentage points is reported from these models. This result suggests that our above-reported results are not a spurious function of pooling data across states, years, and courts. OLS An alternative means of estimating a regression-discontinuity specification is to use OLS regression. This is the estimation procedure used by Lee (2008) in his seminal study of the incumbency advantage in U.S. House elections. While we report estimates based on local linear regression in the text due to possible pathologies with OLS estimation (Gelman and Imbens 2018), as well as the large number of researcher degrees-of-freedom associated with selection of bandwidths and polynomial orders, we nevertheless seek to demonstrate that our results are robust to this alternative estimation strategy. The specification for OLS estimation of our RD design is as follows, ( ) K DemShare i,t+1 = βdemwin i t + ΓDemWin i t (DemShare i t 0.5) k k=0 ( K + Ψ ) (DemShare i t 0.5) k + ɛ i t k=0 where β gives the treatment effect of narrow victory at the cutpoint, and K is the order of the polynomial fit of the running variable, the slope of which is allowed to vary on either side of the cutpoint. In addition to the choice of polynomial fit, there is also the selection of the bandwidth to take into account. As above, we present results across a variety of bandwidth fits. 19

21 Our results for this specification are presented in Figure C.3 in the Supplementary Materials. For each bandwidth ranging from 1% to 20%, at 1% intervals, we estimate the above specification for values of K from one to four. Of these eighty specifications, all produce positive estimates of the incumbency advantage, with the lowest estimate being twelve percentage points. All but eight of the specifications return an estimate that is significant at p < 0.05, and all but five produce estimates that are significant at p < The insignificant results are overwhelmingly from specifications that are underpowered from using little data, high polynomial orders, or most commonly a combination of the two. Overall, the point estimates accord extremely well with those presented above, suggesting that our results are not sensitive to the estimation approach that we use. Randomization Inference Finally, we use an entirely different method of estimating the regression discontinuity design based on an alternative identification assumption. While the regressiondiscontinuity design is identified under a continuity" assumption, in which it is assumed that treated and untreated potential outcomes counterfactually continue smoothly across the cutpoint, a common alternative assumption is a local randomization" assumption. This stronger assumption holds that, within some narrow bandwidth around the cutpoint, observations are asgood-as randomly assigned to treatment and control. In this scenario, rather than estimating a smooth curve, one can simply conduct a difference-in-means test; because of the tighter windows of data used, and subsequent smaller number of observations, randomization inference is used to carry out hypothesis testing (Cattaneo, Frandsen, and Titiunik 2015; Cattaneo, Titiunik, and Vazquez-Bare 2016). To once again probe the robustness of our results, we re-estimate our RD design using this alternative estimation strategy. For bandwidths ranging from one-half of a percentage point to ten percentage points, we estimate the difference in means above and below the cutpoint; in all specifications the sharp null of no effect for any unit is rejected at any conventional level, and 20

22 the estimates are consistent with those presented above. These results are presented in Table C.1 in the Supplementary Materials. These results provide, under an entirely different identifying assumption and estimation strategy, further confidence in the soundness of our results. Conclusion Judicial elections provides Americans with an opportunity to hold their judges accountable for their behavior that citizens in almost every other democracy lack. Yet limitations to the public s ability to exercise oversight over elected judges are readily apparent. Voter engagement, information about candidates positions and incumbents behavior while in office, off-cycle elections and securing quality candidates challenges in nearly every electoral context are seemingly magnified in the judicial arena. In this paper, we contribute new evidence about the degree of competitiveness of judicial elections in the American states. With an extensive dataset of partisan contested elections across over 1,300 seats in six U.S. states, our study reveals low levels of electoral competition across a series of metrics. Importantly, our empirical strategy a regression discontinuity design provides us with leverage to causally identify the electoral advantage that incumbent judges hold due to their status as an officeholder. Our findings show that judges in the American states benefit from a substantial incumbency advantage, with judicial candidates whose party won the previous election estimated to receive over twenty percentage points greater vote totals than those whose party lost the previous election. Our results are robust across states, office types and a series of methodological specifications. We conclude with a consideration of unresolved questions and possibilities for further research. In particular, despite the normative concerns that accompany low levels of competition and a high incumbency advantage, we wish to take a note of caution when interpreting our findings. While much literature stemming from legislative settings highlights the incumbency 21

23 advantage s negative role in attenuating election s capacity to hold legislators accountable, it is also worth considering that retaining incumbents in office can result in beneficial outcomes. The start-up costs necessary to adjust to life on the judicial bench suggest that newcomer judges may be less efficient that their senior colleagues (Hagle 1993; Hettinger, Lindquist, and Martinek 2003). Given the importance of productivity and caseload management in the often understaffed lower courts, long tenure on the bench could have important consequences for the day-to-day function of the institution. Research from the federal courts suggests that in multi-member panels, senior judges curry greater deference than junior judges, suggestive evidence that a voter s ideological preferences may be better represented by an incumbent judge than even a more ideologicallyproximate challenger. While making a case for the incumbency advantage as a problematic phenomenon in legislative elections is bolstered by normative beliefs in programmatic, ideologically distinct parties, dimensions of quality and competence, as well as risk aversion, that may be related to the incumbency advantage may be more normatively desirable in a judicial setting. To close, we note that our analysis has some key limitations. Our focus on partisan, singleseat elections with competitive elections for incumbents provides a stringent test for the competitiveness of judicial elections and allows us to apply conventional methods to estimate the incumbency advantage in these settings. Left unexamined, however, are a rich array of judicial electoral institutions nonpartisan elections, retention elections, high courts each with their own implications for the ability of the electorate to hold judges accountable for their behavior. Future studies should explore competition and the incumbency advantage in greater depth in these electoral settings, especially considering that many of these institutional variations may well increase the barriers to entry for non-incumbent judges. Relatedly, given the high degree of competition documented in many state high court elections (Hall and Bonneau 2005; Hall 2007b), studies of the role of incumbency in these elections may reveal different patterns than we uncover in our analysis. 22

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29 Supplementary Materials The Incumbency Advantage in Judicial Elections Michael Olson and Andrew Stone Contents A Data Appendix 29 A.1 Sample Details A.2 Descriptive Statistics B Additional Results 32 B.1 Placebo Test Results B.2 Local Linear Results, Table Form B.3 Contested Election Results C Robustness Checks 35 C.1 De-Meaned Outcome C.2 OLS C.3 Randomization Inference

30 A Data Appendix A.1 Sample Details State Alabama Indiana Table A.1: Judicial Election Data: Sample Details Races, Years and Number of Unique Seats in Dataset Circuit Court: 2002, 2004, 2006, 2008, 2010, 2012, 2014, 2016 (152 Seats) County Court: 2002, 2004, 2006, 2008, 2010, 2012, 2014, 2016 (124 Seats) Circuit Court: 2002, 2004, 2006, 2008, 2010, 2012, 2014, 2016 (114 Seats) County Court: 2002, 2004, 2006, 2008, 2010, 2012, 2014, 2016 (151 Seats) Kansas District Court: 1998, 2000, 2002, 2004, 2006, 2008, 2010, 2012, 2014, 2016 (75 Seats) Magistrate Court: 1998, 2000, 2002, 2004, 2006, 2008, 2010, 2012, 2014, 2016 (42 Seats) Missouri Circuit Court: 1996, 1998, 2000, 2002, 2004, 2006, 2008, 2010, 2012, 2014, 2016 (74 Seats) Texas District Court: 1992, 1994, 1996, 1998, 2000, 2002, 2004, 2006, 2008, 2010, 2012 (453 Seats) Criminal District Court: 1992, 1994, 1998, 2002, 2006, 2010, 2014 (2 Seats) Family District Court: 1992, 1994, 1996, 1998, 2000, 2002, 2004, 2006, 2008, 2010, 2012 (33 Seats) West Virginia Circuit Court: 1952, 1960, 1968, 1992, 2000 (81 Seats) Note: Table reports the electoral seats in our dataset by state, seat type and year. 29